1. Field of the Invention
The present invention relates to a musical tone synthesizing apparatus which is suitable for synthesizing musical tones produced from percussion instruments.
b 2. Prior Art
Recently, several kinds of musical tone synthesizing apparatuses are developed such that by activating a simulation model simulating a tone-generation mechanism of the non-electronic musical instrument, the musical tones of the non-electronic musical instrument can be simulated well. Some of these musical tone synthesizing apparatuses are designed to synthesize percussive sounds produced from the percussion instruments. General characteristic of the percussive sounds is inability to sustain sounds, in other words, the percussive sound is rapidly attenuated in tone volume. Hereinafter, the percussive sound having the above-mentioned characteristic will be referred to as "an attenuating sound". As the circuitry to synthesize the attenuating sound, a closed-loop circuitry which contains an adder 1, a delay circuit 2 and a filter 3 as shown in FIG. 17 is known. This type of circuitry is designed on the basis of a so-called delay-feedback-type circuitry.
The delay circuit 2 is configured by a shift register. The shift register provides plural flip-flops of which number (simply referred to as a stage number) is determined responsive to a number of bits of a digital signal which is supplied to the delay circuit 2 from the adder 1. Each of the flip-flop receives a clock which is produced by each sampling period .tau..sub.s. A delay time .tau..sub.p of the delay circuit 2 is equivalent to a result of multiplication in which the sampling period .tau. is multiplied by a stage number N of the shift register, i.e., "N.tau..sub.s ". The filter 3 imparts a desired attenuation characteristic to a signal which circulates through the closed loop.
Meanwhile, an analog signal containing frequency components like a noise signal is modulated by a PCM (i.e., Pulse Code Modulation) technique by each sampling period .tau..sub.s, resulting that a time-series digital signal is obtained. Such time-series digital signal is applied to the musical tone synthesizing apparatus as its input signal. This input signal is supplied to the adder 1, from which it is supplied to the filter 3 by means of the delay circuit 2. Then, the signal is fed back to the adder 1. Thus, the input signal circulates through the closed loop.
When ignoring a phase delay occurring in the filter 3, a time which is required for the input signal to circulate the closed loop once is assumed to be equal to the delay time .tau..sub.p. In this case, the gain of the closed loop has a frequency characteristic of which maximum point is emerged at an integral multiple of a fundamental frequency f1=1/.tau..sub.p. Since the closed-loop gain is slightly smaller than "1", the signal which repeatedly circulates through the closed loop is gradually attenuated in amplitude. During an attenuating process of the signal, the output of the adder 1 is extracted and is subjected to digital-to-analog conversion. Thus, it is possible to obtain an attenuating signal having a fundamental wave and the other higher harmonic waves of which frequencies correspond to integral multiples of the fundamental frequency. By use of the above-mentioned closed loop, it is possible to excite the musical tone signal having the fundamental-wave component and higher-harmonic components like the real musical sound which is produced from the stringed instrument. Such musical tone signal is gradually attenuated in amplitude in a lapse of time.
In the circuitry shown in FIG. 17, the delay time .tau. can be set in response to the integral multiple of the sampling period .tau., in other words, the delay time .tau. cannot be arbitrarily changed other than the delay times each corresponding to the integral multiple of the sampling period. In order to obtain an arbitrary delay time which is shifted from the delay time corresponding to the integral multiple of the sampling period .tau..sub.s, an all-pass filter 4 must be inserted between the delay circuit 2 and the filter 3 as shown in FIG. 18. This all-pass filter 4 is designed on tile basis of the known configuration of the primary digital filter. It is configured by adders 41, 42, multipliers 43, 44 and a delay circuit 45. As similar to the delay circuit 2, the delay circuit 45 receives a clock by each sampling period .tau..sub.s.
In the all-pass filter 4, the output of the delay circuit 2 is added with an output of the multiplier 44 by the adder 41. The output of the adder 41 is delivered to the adder 42 by means of the delay circuit 45. In addition, the output of the adder 41 is also delivered to the multiplier 43 wherein it is multiplied by a multiplication coefficient "-.alpha.". Then, a result of the multiplication performed by the multiplier 43 is supplied to the adder 42. On the other hand, the multiplier 44 multiplies the output of the delay circuit 45 by a multiplication coefficient ".alpha.", and then, a result of the multiplication performed by the multiplier 44 is supplied to the adder 41. The adder 42 adds the output of the delay circuit 45 to the output of the multiplier 43. A result of the addition is outputted to the filter 3. As each of the multiplication coefficients ".alpha." and "-.alpha." which are respectively used in the multipliers 43 and 44, it is possible to use a value which exists between "-1" and "1".
The function of the all-pass filter 4 described above can be expressed by use of a transfer function H(z) which is denoted by an equation (1) as follows: EQU H(z)=.alpha.+z.sup.-1 /1+.alpha.z.sup.-1 (1)
By replacing the term "z" by another term "exp(-j.omega..tau..sub.s)" in the equation (1), it is possible to obtain an equation (2), which represents a frequency characteristic F(.omega.) of the all-pass filter 4. EQU F(.omega.)=.alpha.+exp(-j.omega..tau..sub.s)/1+.alpha.*exp('j.omega..tau..s ub.s) (2)
A gain-frequency characteristic G(.omega.) of the all-pass filter 4 becomes equal to an absolute value of the above-described equation (2) as follows: EQU G(.omega.)=.vertline.F(.omega.).vertline.=1.
Thus, the gain of the all-pass filter 4 is maintained at "1" in all of the frequency bands. This is the reason why this type of filter is called as the all-pass filter. Under the condition where an angular frequency .omega. is relatively low as compared to the Nyquist's angular frequency .omega.n=2.pi.fs/2 (where fs is the sampling frequency) and a phase angle .omega..tau..sub.s is close to "0", a phase delay P(.omega.) can be expressed by the following approximate expression (3). EQU P(.omega.).apprxeq.(1-.alpha.).omega..tau..sub.s /(1+.alpha.) (3)
An equivalent delay time .tau..sub.a of the all-pass filter 4 is expressed by the following equation (4). EQU .tau..sub.a =P(.omega.)/.omega. (4)
By use of the aforementioned equation (3), the delay time .tau..sub.a can be approximated as follows: EQU .tau..sub.a .apprxeq.(1-.alpha.).tau..sub.s /(1+.alpha.).
This approximate expression indicates that the delay time .tau..sub.a of the all-pass filter 4 can be adjusted by changing the multiplication coefficient .alpha..
In result, the closed loop which consists of the circuit elements 1 to 4 as shown in FIG. 18 may have a resonance characteristic which responds to a whole delay time .tau. (where .tau.=.tau..sub.p +.tau..sub.a). Next, the resonance characteristic of the closed loop will be described by referring to FIGS. 19(A) to 19(C). FIG. 19(A) shows a relationship between a frequency f and a phase delay .theta. in connection with the delay circuit 2 (see FIG. 18). As shown in FIG. 19(A), when the frequency f of the signal passing through the delay circuit 2 becomes equal to f1 (where f1=1/.tau..sub.p), the phase difference .theta. existing between the phases of the input signal and output signal of the delay circuit 2 becomes equal to 2.pi.. The phase difference .theta. turns to 4.pi. when the frequency f is equal to f2 which is twice as large as the frequency f1, while the phase difference .theta. turns to 6.pi. when the frequency f is equal to f3 which is a triple of the frequency f1. In short, the phase delay .theta. is linearly changed with respect to the frequency f as shown by a straight line A shown in FIG. 19(A). When the frequency f becomes equal to the integral multiple of the fundamental frequency, the phase of the input signal coincides with that of the output signal.
FIG. 19(B) shows a relationship between the frequency f and the phase delay .theta. in the all-pass filter 4. According to the aforementioned equation (3), the phase delay .theta. is approximately varied along with a linear curve with respect to the frequency f under the condition where the frequency f is sufficiently lower than the Nyquist's frequency 1/2.tau..sub.s. However, when varying the frequency f in a wide range including the Nyquist's frequency 1/2.tau..sub.s, the phase delay .theta. is varied along with a curve B shown in FIG. 19(B).
Therefore, a resonant frequency of the musical tone synthesizing apparatus is changed responsive to the whole phase delay of the closed loop which is obtained by adding the phase delay of the delay circuit 2 (see FIG. 19(A)) with the phase delay of the all-pass filter 4 (see FIG. 19(B)). FIG. 19(C) is a graph showing a delay characteristic of the closed loop as a whole (see a curve C). Due to the insertion of the all-pass filter 4 into the closed loop, the phase delay .theta. becomes equal to 2.pi., 4.pi., 6.pi. at respective frequencies f1a, f2a, f3a which are respectively shifted from the aforementioned frequencies f1, f2, f3.
In the case where the frequency f of the signal coincides with each of the frequencies f1a, f2a, f3a, . . . , the phase of the signal is not changed at all even if the signal circulates the closed loop once. At these frequencies, the gain of the closed loop becomes maximum, in other words, the closed loop is set in a resonating state. Since a non-linear relationship is established between the frequency f and the phase delay .theta., an interval between adjacent two of the frequencies f1a, f2a, f3a, . . . cannot be maintained constant. Thus, the insertion of the all-pass filter 4 enables the closed loop to synthesize the musical tones having an overtone structure. In the overtone structure, higher harmonics of which frequencies are not equal to the integral multiple of the fundamental frequency are contained in the musical tone. As described before, by changing the multiplication coefficient .alpha., the resonant frequency of the closed loop can be changed, resulting that the tone pitch of the attenuating sound corresponding to the signal circulating through the closed loop can be controlled. As another method to control the tone pitch of the musical tone to be synthesized by the musical tone synthesizing apparatus, it is possible to employ a weighted interpolation which is effected on each of the delay stages of the delay circuit 2 so as to control the delay time .tau..sub.p.
As described above, the conventional musical tone synthesizing apparatus can control the tone pitch in response to a variation of the delay amount of the closed loop which is carried out by changing the multiplication coefficient .alpha. of the all-pass filter 4. However, this type of the musical tone synthesizing apparatus suffers from the following drawbacks. When largely changing the multiplication coefficient .alpha. of the all-pass filter 4, the whole delay amount of the closed loop must be largely varied. In that case, the apparatus synthesizes a non-harmonious musical tone containing a plenty of higher harmonics of which number is larger than the necessary number of the higher harmonics. As a result, this type of the musical tone synthesizing apparatus is not suitable for the electronic musical instrument. A control of the delay amount which is controlled by changing the multiplication coefficient .alpha. of the all-pass filter 4 is effective only when the delay circuit 2 provides one or two delay stages. Further, when changing the multiplication coefficient .alpha. while also changing the number of the delay stages of the delay circuit 2, the multiplication coefficient .alpha. should be changed discontinuously, which may cause a production of noises.
In another type of the apparatus in which the weighted interpolation is effected on each of the delay stages of the delay circuit 2 so as to control the delay time .tau..sub.p, the tone pitch can be controlled in a relatively wide range. However, the interpolation of the delay stages causes an operation of a low-pass filter, which deteriorates the frequency characteristic of the musical tone to be synthesized. In addition, this type of the apparatus also suffers from a disadvantage in that an attenuation time of the attenuating sound must be changed responsive to the control of the tone pitch. In short, the conventional musical tone synthesizing apparatus providing the all-pass filter 4 cannot alter the delay amount smoothly without causing a variation of the amplitude of the musical tone. In other words, the conventional apparatus suffers from a problem in that the tone pitch of the attenuating sound cannot be controlled to be altered continuously.